Problem: Solve for $x$ : $5\sqrt{x} - 6 = 7\sqrt{x} + 8$
Answer: Subtract $5\sqrt{x}$ from both sides: $(5\sqrt{x} - 6) - 5\sqrt{x} = (7\sqrt{x} + 8) - 5\sqrt{x}$ $-6 = 2\sqrt{x} + 8$ Subtract $8$ from both sides: $-6 - 8 = (2\sqrt{x} + 8) - 8$ $-14 = 2\sqrt{x}$ Divide both sides by $2$ $\frac{-14}{2} = \frac{2\sqrt{x}}{2}$ Simplify. $-7 = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.